\[ x y'(x)-y(x) f(x y(x))=0 \] ✓ Mathematica : cpu = 0.253086 (sec), leaf count = 115
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {1}{(-f(x K[2])-1) K[2]}-\int _1^x\left (\frac {f'(K[1] K[2])}{f(K[1] K[2])+1}-\frac {f(K[1] K[2]) f'(K[1] K[2])}{(f(K[1] K[2])+1)^2}\right )dK[1]\right )dK[2]+\int _1^x\frac {f(K[1] y(x))}{(f(K[1] y(x))+1) K[1]}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.03 (sec), leaf count = 29
\[\left \{y \left (x \right ) = \frac {\RootOf \left (c_{1}+\int _{}^{\textit {\_Z}}\frac {1}{\left (f \left (\textit {\_a} \right )+1\right ) \textit {\_a}}d \textit {\_a} -\ln \left (x \right )\right )}{x}\right \}\]